Stability of difference schemes for convection-diffusion problems (Q1974739)

The authors obtain sufficient conditions of stability in the spaces \(L_\infty\) and \(L_1\) by involving the concept of the logarithmic norm of an operator. He considers the two layer difference scheme for a set of ordinary differential equations. The authors apply the general conditions obtained for a two-dimensional model convection-diffusion equation with convective forms written in either conservative or nonconservative form. Upwind and central difference schemes are considered as approximations of the convective-transfer terms.